Difference between revisions of "1999 IMO Problems/Problem 6"
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− | + | ==Problem== | |
− | + | ||
+ | Determine all functions <math>f:\Bbb{R}\to \Bbb{R}</math> such that | ||
+ | |||
+ | <cmath>f(x-f(y))=f(f(y))+xf(y)+f(x)-1</cmath> | ||
+ | |||
+ | for all real numbers <math>x,y</math>. | ||
+ | |||
+ | ==Solution== | ||
+ | {{solution}} | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=1999|num-b=5|after=Last Question}} | ||
+ | |||
+ | [[Category:Olympiad Algebra Problems]] | ||
+ | [[Category:Functional Equation Problems]] |
Latest revision as of 00:02, 19 November 2023
Problem
Determine all functions such that
for all real numbers .
Solution
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See Also
1999 IMO (Problems) • Resources | ||
Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
All IMO Problems and Solutions |